A mathematical model for predicting bubble growth for low Bond and Jakob number nucleate boiling

In an effort to better understand the physical mechanisms responsible for pool boiling heat transfer, an analytical model is developed that describes the changing shape and size of a growing vapour bubble in a non-uniform temperature field. Indeed, any analysis of thermal transport due to nucleate pool boiling requires bubble frequency predictions which are intimately linked to bubble growth characteristics such as volume and time of detachment from the nucleation site. The model is developed and validated for quasi-static bubble growth due to vaporization within the heat-transfer controlled growth regime. It highlights the need to include the asymmetric nature of growing bubbles when modeling bubble growth and it accounts for the movement of the thermal boundary layer in the bubble׳s vicinity.Analysis of previously published numerical treatments of bubble shape evolution leads to simplifying bubble geometry for low Bond number applications. The geometric model accounts for bubble shape transformation throughout the bubble growth cycle. It is idealized as a segmented sphere atop a cylindrical neck. An analytical model of quasi-static diabatic bubble growth is accordingly developed and is coupled with a geometric detachment relation and a force balance detachment criterion that are dependent on the Bond number.The resultant low Bond number bubble evolution model is validated with images of n-pentane vapour bubble formations issuing from an artificial cavity. In order to solve the mass–energy balance at the vapour bubble interface, a spherical surface area is commonly assumed. This leads to the need for correction factors and provides little insight into the physical mechanism responsible for bubble shape. In this study, the transitioning shape of a vapour bubble is considered in the integral analysis of the interfacial mass–energy balance. The model predicts the following bubble growth and detachment characteristics: profile, volume, center of gravity, bubble height, Aspect Ratio and moment of detachment.